# Anomalous magnetic moment of the muon, a hybrid approach

C. A. Dominguez, H. Horch, B. Jäger, N. F. Nasrallah, K. Schilcher, H. Spiesberger, H. Wittig

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## Abstract

A new QCD sum rule determination of the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, $a_{\mu}^{\rm hvp}$, is proposed. This approach combines data on $e^{+}e^{-}$ annihilation into hadrons, perturbative QCD and lattice QCD results for the first derivative of the electromagnetic current correlator at zero momentum transfer, $\Pi_{\rm EM}^\prime(0)$. The idea is based on the observation that, in the relevant kinematic domain, the integration kernel $K(s)$, entering the formula relating $a_{\mu}^{\rm hvp}$ to $e^{+}e^{-}$ annihilation data, behaves like $1/s$ times a very smooth function of $s$, the squared energy. We find an expression for $a_{\mu}$ in terms of $\Pi_{\rm EM}^\prime(0)$, which can be calculated in lattice QCD. Using recent lattice results we find a good approximation for $a_{\mu}^{\rm hvp}$, but the precision is not yet sufficient to resolve the discrepancy between the $R(s)$ data-based results and the experimentally measured value.
Original language English 074016 Physical Review D 96 7 8 2470-0010 https://doi.org/10.1103/PhysRevD.96.074016 Published - 2017

### Bibliographical note

14 pages, added some clarifying text and two references, removed typos, results unchanged. Version to be published in Phys.Rev.D